We will also take into consideration only the metric formulation of \(f(R)\)  gravity in which the only dynamical degree of freedom is the metric and the affine connection is a function of the metric and it's first derivatives. Another formulation of \(f(R)\)  gravity is the so-called Palatini formulation, which treats the metric and the affine connection as two independent dynamical quantities. For general relativity (GR) the two formalisms produce the same field equations but for \(f(R)\)  gravity they produce different field equations. For an interesting connection between these two formulations, see Ref.[1]}.
